A note on area estimates for stable $H$-hypersurfaces and applications

Author:

Marcos Ranieri, Elaine Sampaio, Feliciano Vitório

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-05-03 16:00:00

Abstract

We show some area estimates for stable CMC hypersurfaces immersed in Riemannian manifolds with scalar and sectional curvature bounded from below. In particular, we focus on immersions in three-dimensional Riemannian manifolds. As an application, we derive some upper estimates for the bottom spectrum of these hypersurfaces. This paper generalizes and builds on the techniques developed by Munteanu, Sung and Wang for stable minimal surfaces.

PDF: A note on area estimates for stable $H$-hypersurfaces and applications.pdf